I think this thought that every team gives their best against us, meaning the Cowboys, is highly over-rated. In the NFL, you only have 16 opportunities to win and most if not all teams give their best regardless of who they are playing. I doubt the Commanders effort against the Giants this week is somehow going to be less than when they played the Cowboys last week.
Maybe this was more relevant back in the days when the Cowboys built these dynasty type teams that everyone wanted to knock off, but to be honest, the Cowboys the last 20 years or so have just been your average NFL team.